CN101739670A - Non-local mean space domain time varying image filtering method - Google Patents

Abstract

The invention discloses a non-local mean space domain time varying image filtering method, mainly solving the problem that the existing non-local mean space domain time varying filter is large in computation amount and restricted in application range. The filtering process includes that: weight normalization coefficient and value after non-normalization filtering at all the points of the original image are initialized to be zero; for polarization of each coordinate in search domain, all the pixel points of the original image are subject to uniform pre-treatment, then a weighting verifying value of all the pixel points of the original image at the coordinate in the search domain is rapidly calculated; the weight normalization coefficient and the value after non-normalization filtering are updated according to the weighting verifying value; and the image after filtering is obtained by calculation according to the weight normalization coefficient and the value after non-normalization filtering. The invention greatly reduces the computational complexity of the existing non-local mean space domain time varying filtering method and can be applicable to the image restoring, image de-noising and image super resolution rebuilding fields.

Description

Non-local mean space domain time varying image filtering method

Technical field

The invention belongs to image processing field, relate to image filtering method, specifically a kind of non-local mean space domain time varying image filtering method is used for the processing to digital picture and video image.

Technical background

Along with information and Development of Multimedia Technology, the application of digital image processing techniques more and more widely.The airspace filter technology is one of basic skills of Digital Image Processing, has a wide range of applications in the digital picture field, such as image recovery, image denoising, image super-resolution rebuilding etc.The basic thought of airspace filter is to utilize the relation between the adjacent pixels point to obtain corresponding processing intent.The shape that the pixel that closes on is formed is called as region of search.For any pixel in the image, this put the filtered value region of search that to equal with this point be the center carry out value after normalization weighting and the summation a little.If use I,

Represent the image behind original image and the airspace filter respectively, then have the basic representation of spatial domain wave filter to be:

$\hat{I}(x,y)=\frac{1}{\mathrm{\α}(x,y)}\underset{(u,v)\∈V_R}{\mathrm{\Σ}}w(x,y,u,v)I(x+u,y+v),$

Wherein, V _RBe the region of search that adjacent pixels point is formed, u, v are V _RInterior row, column coordinate, x, y are respectively the row, column coordinate of pixel, w (u v) is a weighting nuclear for x, y, $\mathrm{\α}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}w(x,y,u,v)$ It is normalization coefficient.When weighting nuclear w (u v) is one and x for x, y, during the irrelevant fixed function of y, constant filtering when deserving to be called the process of stating and being the spatial domain; (u v) is one and x for x, y, and during the relevant variation function of y, deserving to be called the process of stating is space domain time varying filtering as weighting nuclear w.

The non-local mean wave filter is the space domain time varying wave filter that is proposed in article " Areview of imagedenoising algorithms, with a new one " by people such as Buades.Non-local mean wave filter region of search is that radius is the rectangular window of R, promptly $V_R\stackrel{\mathrm{\Δ}}{=}\{(u,v):-R\≤u,v\≤R,u,v\∈N\},$ The weighting nuclear of non-local mean wave filter $w(x,y,u,v)=\exp (-\frac{S(x,y,u,v)}{2h^p}),$ Wherein, S (u v) is called image biasing similar function for x, y, $S(x,y,u,v)={\left|\right|B_r(x,y)-B_r(x+u,y+v)\left|\right|}_p^p,$ H is a weighting nuclear width, || || _p ^pExpression l _pThe p power of norm value, p 〉=1, exp () is an exponential function, B _r(x is y) for representing so that (x y) is the center, is the matching window of the rectangular block of radius with r.

Referring to Fig. 1, existing non-local mean space domain time varying image filtering flow process is:

[1] obtains original image information, relatively norm parameter p of region of search shape, matching window shape, weighting nuclear width h and similarity is set;

[2] to each coordinate points in the original image, filtering is carried out in execution in step [3]～[6] respectively;

[3], calculate corresponding weighting nuclear weights respectively to each pixel in the region of search that is the center with current filtering coordinate in the original image:

$w(x,y,u,v)=\exp (-\frac{S(x,y,u,v)}{2h^p}),$

Wherein, (u v) is the region of search coordinate, S (x, y, u, v)=|| B _r(x, y)-B _r(x+u, y+v) || _p ^p

[4] calculate all weightings nuclear weights in the prime field scope of searching that current filtering coordinate in the original image is the center and, obtain normalization coefficient;

[5] calculating in the original image with current filtering coordinate is searching in the prime field of center, the weights of each pixel correspondence multiply by the corresponding point value of information and, as the non-normalized filtered value at current filtering coordinate place;

[6] with in the original image in the non-normalized filtered value at current filtering coordinate place divided by normalization coefficient, obtain the filtered value at current filtering coordinate place;

[7] all filtered values in coordinate place are formed filtered image.

Above-mentioned non-local mean filtering method is in the image bias function of calculating adjacent pixels point and region of search bias combination, the phenomenon that the images match window covers can appear, thereby can cause the matching window interior pixel point that covers and add region of search setovering between the combination of pixels, repeatedly carry out the calculating redundancy issue that relatively calculates.And above-mentioned non-local mean wave filter in the pointwise filtering, the weighting of each region of search bias point of each pixel nuclear weights all need to recomputate, and can cause a large amount of double countings like this.If the image size is M * N, then the computation complexity of non-local mean filtering needs is O[(2r+1) ²(2R+1) ²MN].This great computation complexity causes computing time long, has limited the application of non-local mean wave filter greatly, such as the non-local mean filtering method that just can not use this computation complexity in real time embedded system.

Summary of the invention

The objective of the invention is to overcome the problem of above-mentioned prior art, propose a kind of non-local mean space domain time varying image filtering method,, enlarge the range of application of non-local mean wave filter to reduce the computation complexity of non-local mean space domain time varying wave filter.

Realize that technical thought of the present invention is: for each coordinate in the region of search, respectively that original image is all pixels carry out unified pre-service, calculate the weighting nuclear weights of all pixels of original image at this region of search coordinate place then; Weighting nuclear weights according to each point of original image of all coordinate place correspondences of region of search calculate filtered image information.Its specific implementation is as follows:

Technical scheme 1, a kind of non-local mean space domain time varying image filtering method, it comprises the steps:

(1) obtains original image information, relatively norm parameter p of region of search shape, matching window size, weighting nuclear width h and similarity is set;

(2) the non-normalized filtered image I of initialization (x, y) (x y) is 0, and wherein (x y) is image coordinate with weights normalization coefficient α;

(3) with the point in the region of search as biasing, to the operation of a have execution in step (4)～(9);

(4) (u v) is an amount of bias, calculates the value of the p power of the absolute value of the data difference of all corresponding point between original image and the biasing back image, obtains p norm error image Δ with current biasing ^{(u, v)}(x, y);

(5) (u v) descends the error image Δ to calculate current biasing ^{(u, v)}(x, integral image S y) ^{(u, v)}(x, y), computing formula is:

$S^{(u,v)}(x,y)=\underset{y^{\′}\≤y}{\mathrm{\Σ}}\underset{x^{\′}\≤x}{\mathrm{\Σ}}{\mathrm{\Δ}}^{(u,v)}(x^{\′},y^{\′});$

(6) by following formula calculate current biasing coordinate (u, the v) image at each coordinate place of under the original image similar function value of setovering:

D (x, y, u, v)=S ^{(u, v)}(x _l, y _t)+S ^{(u, v)}(x _r, y _b)-S ^{(u, v)}(x _l, y _b)-S ^{(u, v)}(x _r, y _t), wherein, (x y) is image coordinate, (x _l, y _t), (x _r, y _b) represent respectively with (x, y) upper left corner coordinate of the matching window at center and lower right corner coordinate;

(7) by following formula calculate current biasing (u, v) down, the weighting at each coordinate place of original image nuclear weights:

$w(x,y,u,v)=\exp (-\frac{D(x,y,u,v)}{2h^p}),$

Wherein, (u v) is weighting nuclear weights to w for x, y, and h is a weighting nuclear width, and exp () is an exponential function;

(8) current biasing coordinate (u, v) down, upgrade the weights normalization coefficient at each coordinate place of original image by following formula:

α(x，y)＝α(x，y)+w(x，y，u，v)，

Wherein, (x y) is normalization coefficient to α;

(9) under current biasing coordinate, upgrade the non-normalized filtered value at each coordinate place of original image by following formula:

I(x，y)＝I(x，y)+w(x，y，u，v)×I(x+u，y+v)，

Wherein, (x y) is non-normalized filtered value to I, and I is an original image information;

(10) by following formula each coordinate of original image is carried out normalized, obtain image after the filtering

$\hat{I}(x,y)=\frac{\stackrel{\‾}{I}(x,y)}{\mathrm{\α}(x,y)}.$

Technical scheme 2, a kind of non-local mean space domain time varying image filtering method comprises the steps:

1) obtains original image information, relatively norm parameter p of region of search shape, matching window size, weighting nuclear width h and similarity is set;

2) with the point in the region of search as biasing, to a have execution in step 3)～6) operation;

3) (u v) is an amount of bias, calculates the value of the p power of the absolute value of the data difference of all corresponding point between original image and the biasing back image, obtains p norm error image Δ with current biasing ^{(u, v)}(x, y), wherein (x y) is image coordinate;

4) (u v) descends the error image Δ to calculate current biasing ^{(u, v)}(x, integral image S y) ^{(u, v)}(x, y), computing formula is:

$S^{(u,v)}(x,y)=\underset{y^{\′}\≤y}{\mathrm{\Σ}}\underset{x^{\′}\≤x}{\mathrm{\Σ}}{\mathrm{\Δ}}^{(u,v)}(x^{\′},y^{\′});$

5) by following formula calculate current biasing coordinate (u, the v) image at each coordinate place of under the original image similar function value of setovering:

D (x, y, u, v)=S ^{(u, v)}(x _l, y _t)+S ^{(u, v)}(x _r, y _b)-S ^{(u, v)}(x _l, y _b)-S ^{(u, v)}(x _r, y _t), wherein, (x y) is image coordinate, (x _l, y _t), (x _r, y _b) represent respectively with (x, y) upper left corner coordinate of the matching window at center and lower right corner coordinate;

6) by following formula calculate current biasing (u, v) down, the weighting at each coordinate place of original image nuclear weights:

$w(x,y,u,v)=\exp (-\frac{D(x,y,u,v)}{2h^p}),$

Wherein, (u v) is weighting nuclear weights to w for x, y, and h is a weighting nuclear width, and exp () is an exponential function;

7) by following formula calculate each coordinate place of original image weights normalization coefficient α (x, y):

$\mathrm{\α}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}w(x,y,u,v),$

Wherein, (u v) is the coordinate in the region of search, V _RBe the region of search shape, and w (x, y, u, v j) is weighting nuclear weights;

8) by following formula calculate to calculate each coordinate place of original image non-normalized filtered value I (x, y):

$\stackrel{\‾}{I}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}[w(x,y,u,v)\×I(x+u,y+v)],$

Wherein, I is an original image information;

9) by following formula each coordinate of original image is carried out normalized, obtain image after the filtering

$\hat{I}(x,y)=\frac{\stackrel{\‾}{I}(x,y)}{\mathrm{\α}(x,y)}.$

The present invention has following advantage:

(1) existing non-local mean space domain time varying filtering method is when calculating the weighting nuclear weights of adjacent pixels point and region of search bias combination, the phenomenon that the images match window covers can appear, thereby can cause the matching window interior pixel point that covers and add region of search setovering between the combination of pixels, repeatedly carry out the calculating redundancy issue that relatively calculates.And the present invention is because for each biasing coordinate in the region of search, adopt step (4)～(7) of technical scheme 1 or step 3)～6 of technical scheme 2), for each pixel with add region of search biasing combination of pixels, only calculate once relatively calculating operation, that has eliminated that existing non-local mean space domain time varying filtering method exists covers the problem of the calculating redundancy that causes by matching window.So non-local mean space domain time varying image filtering method that the present invention proposes, under the situation that does not influence filtering performance, greatly reduce the calculated amount of existing non-local mean space domain time varying filtering method, accelerated filtering speed, widened the range of application of non-local mean wave filter.

Description of drawings

Fig. 1 is existing non-local mean space domain time varying image filtering method process flow diagram;

Fig. 2 is the image filtering method process flow diagram of technical solution of the present invention 1;

Fig. 3 is the image filtering method process flow diagram of technical solution of the present invention 2;

Fig. 4 is among Fig. 2 and Fig. 3, calculates the sub-process figure of original image all weights under current biasing coordinate;

Fig. 5 generates biasing image schematic diagram for original image;

Fig. 6 is that figure is described in the rectangular area in the error image;

Fig. 7 is when p=1, the filtering comparison diagram of the present invention and existing non-local mean space domain time varying filtering method;

Fig. 8 is when p=2, the filtering comparison diagram of the present invention and existing non-local mean space domain time varying filtering method.

Embodiment

Referring to Fig. 2, a kind of non-local mean space domain time varying image filtering method that technical scheme 1 of the present invention proposes comprises the steps:

Step 1 is obtained original image information, and the filtering correlation parameter is set, the non-normalized filtered image I of initialization (x, y) and weights normalization coefficient α (x, y).

The filtering correlation parameter that is provided with comprises relatively norm parameter p of region of search shape, matching window size, weighting nuclear width h and similarity; This region of search is rectangle, triangle, circle or arbitrary polygon, and this matching window is shaped as rectangle, and weighting nuclear width h when being arranged on according to image biasing similar function value calculating weighting nuclear weights and similarity be the norm parameter p relatively; This weighting nuclear width h is any arithmetic number, and this similarity comparison norm parameter p is any nonnegative real number; (x, y) (x y), all is initially 0, and wherein (x y) is image coordinate with weights normalization coefficient α with the value I of each non-normalized filtered image in coordinate place of image.

Step 2, with the point in the region of search as biasing, to of the operation of a have execution in step three to step 5; If in the region of search somewhat equal executed step 3 to the operation of step 5, jump to step 6.

Step 3 under current biasing coordinate, is calculated the weighting nuclear weights at all coordinate points places of original image.

Referring to Fig. 4, the specific implementation of this step is as follows:

3.1) as shown in Figure 5, white box is expressed as original image information I, grey box is for having added (u, v) Pian Zhi image I _s ^{(u, v)}, white box and grey box corresponding region value equate the image I of promptly setovering _s ^{(u, v)}Coordinate (x, the value of y) locating is:

$I_s^{(u,v)}(x,y)=I(x+u,y+v);$

The error image Δ ^{(u, v)}(x y) calculates by following formula:

Δ ^(u，v)(x，y)＝|I(x，y)-I(x+u，y+v)| ^p，

Wherein I is an original image information, || ^pFor asking the p power operation of absolute value;

3.2) (u v) descends the error image Δ to calculate current biasing ^{(u, v)}(x, integral image S y) ^{(u, v)}(x, y), computing formula is:

$S^{(u,v)}(x,y)=\underset{y^{\′}\≤y}{\mathrm{\Σ}}\underset{x^{\′}\≤x}{\mathrm{\Σ}}{\mathrm{\Δ}}^{(u,v)}(x^{\′},y^{\′});$

3.3) calculate the image biasing similar function value at each the coordinate place of original image under current biasing coordinate by following formula:

D (x, y, u, v)=S ^{(u, v)}(x _l, y _t)+S ^{(u, v)}(x _r, y _b)-S ^{(u, v)}(x _l, y _b)-S ^{(u, v)}(x _r, y _t), wherein (x, y), ((u v) is the image similar function value of setovering, S to D for x, y for u, v) respectively presentation video coordinate and current biasing coordinate ^{(u, v)}Be illustrated in the integral image under the current biasing coordinate, (x _l, y _t), (x _r, y _b) represent respectively so that (the matching window shape is set up in step 1 for x, y) upper left corner coordinate of the matching window shape at center and lower right corner coordinate;

3.4) calculate under current biasing coordinate the weighting at each coordinate place of original image nuclear weights by following formula:

$w(x,y,u,v)=\exp (-\frac{D(x,y,u,v)}{2h^p}),$

Wherein (x, y), ((u v) is weighting nuclear weights to w for x, y, and h is that width is examined in weighting, and exp () is an exponential function for u, v) respectively presentation video coordinate and current biasing coordinate.

Step 4, current biasing coordinate (u, v) down, upgrade the weights normalization coefficient at each coordinate place of original image by following formula:

α(x，y)＝α(x，y)+w(x，y，u，v)，

Wherein, (x y) is normalization coefficient to α.

Step 5, under current biasing coordinate, upgrade the non-normalized filtered value at each coordinate place of original image by following formula:

I(x，y)＝I(x，y)+w(x，y，u，v)×I(x+u，y+v)，

Wherein, (x y) is non-normalized filtered value to I, and I is an original image information.

By step 2 to five, calculated non-normalized filtered image I (x, y) and weights normalization coefficient α (x, y).

Step 6 is carried out normalized by following formula to each coordinate of original image, obtains image after the filtering

$\hat{I}(x,y)=\frac{\stackrel{\‾}{I}(x,y)}{\mathrm{\α}(x,y)}.$

Technique scheme 1 described image filtering method, the order of wherein said step 4 and step 5 can be exchanged.

Technique scheme 1 described image filtering method, wherein step 3 to five and step 6 use serial mode, parallel mode or serial to calculate with parallel mode of mixing.

The digital picture of the original image that technique scheme 1 method is handled for directly collecting, or through the digital picture after certain processing.

Technique scheme 1 can be applied to be similar in the airspace filter method of non-local mean filter weight nuclear weight calculation method.Step 3.1) in, error image can be obtained by any elementary mathematics conversion between all corresponding point between original image and the biasing image.Step 3.4) in, weighting nuclear weights can obtain by image biasing similar function value is done any elementary mathematics conversion.

The filtering of technique scheme 1 also can be realized with the step of following technical proposals 2.

Referring to Fig. 3, a kind of non-local mean space domain time varying image filtering method that technical solution of the present invention 2 proposes comprises the steps:

Step 1 is obtained original image information, and the filtering correlation parameter is set.

The filtering correlation parameter that is provided with comprises relatively norm parameter p of region of search shape, matching window size, weighting nuclear width h and similarity; This region of search is rectangle, triangle, circle or arbitrary polygon, and this comparison domain is shaped as rectangle; Weighting nuclear width h when being arranged on according to image biasing similar function value calculating weighting nuclear weights and similarity be the norm parameter p relatively; This weighting nuclear width h is any arithmetic number, and this similarity comparison norm parameter p is any nonnegative real number.

Step 2, is operated a have execution in step 3 as biasing with the point in the region of search; If somewhat equal executed step 3 operation of institute jumps to step 4 in the region of search.

Step 3 under current biasing coordinate, is calculated the weighting nuclear weights at all coordinate points places of original image.

Referring to Fig. 4, the specific implementation of this step is as follows:

3a) as shown in Figure 5, white box is expressed as original image information I, and grey box is for having added (u, v) Pian Zhi image I _s ^{(u, v)}, white box and grey box corresponding region value equate the image I of promptly setovering _s ^{(u, v)}Coordinate (x, the value of y) locating is:

$I_s^{(u,v)}(x,y)=I(x+u,y+v);$

The error image Δ ^{(u, v)}(x y) calculates by following formula:

Δ ^(u，v)(x，y)＝|I(x，y)-I(x+u，y+v)| ^p，

Wherein I is an original image information, || ^pFor asking the p power operation of absolute value;

(u v) descends the error image Δ 3b) to calculate current biasing ^{(u, v)}(x, integral image S y) ^{(u, v)}(x, y), computing formula is:

$S^{(u,v)}(x,y)=\underset{y^{\′}\≤y}{\mathrm{\Σ}}\underset{x^{\′}\≤x}{\mathrm{\Σ}}{\mathrm{\Δ}}^{(u,v)}(x^{\′},y^{\′});$

3c) calculate the image biasing similar function value at each the coordinate place of original image under current biasing coordinate by following formula:

D (x, y, u, v)=S ^{(u, v)}(x _l, y _t)+S ^{(u, v)}(x _r, y _b)-S ^{(u, v)}(x _l, y _b)-S ^{(u, v)}(x _r, y _t), wherein (x, y), ((u v) is the image similar function value of setovering, S to D for x, y for u, v) respectively presentation video coordinate and current biasing coordinate ^{(u, v)}Be illustrated in the integral image under the current biasing coordinate, (x _l, y _t), (x _r, y _t) represent respectively so that (the matching window shape is set up in step 1 for x, y) upper left corner coordinate of the matching window shape at center and lower right corner coordinate;

3d) calculate under current biasing coordinate the weighting at each coordinate place of original image nuclear weights by following formula:

$w(x,y,u,v)=\exp (-\frac{D(x,y,u,v)}{2h^p}),$

Wherein (x, y), ((u v) is weighting nuclear weights to w for x, y, and h is that width is examined in weighting, and exp () is an exponential function for u, v) respectively presentation video coordinate and current biasing coordinate.

By step 2～3, calculated the weighting nuclear weights at all the coordinates of original image coordinates places under the biasing of each region of search, just obtained each coordinates of original image coordinates and be in all region of search biasing weightings down and examine weights.

Step 4, by following formula calculate each coordinate place of original image weights normalization coefficient α (x, y):

$\mathrm{\α}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}w(x,y,u,v),$

Wherein, (u v) is the coordinate in the region of search, V _RBe the region of search shape, and w (x, y, u, v j) is weighting nuclear weights.

Step 5, by following formula calculate to calculate each coordinate place of original image non-normalized filtered value I (x, y):

$\stackrel{\‾}{I}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}[w(x,y,u,v)\×I(x+u,y+v)].$

Step 6 is carried out normalized by following formula to each coordinate of original image, obtains image after the filtering

$\hat{I}(x,y)=\frac{\stackrel{\‾}{I}(x,y)}{\mathrm{\α}(x,y)}.$

Technique scheme 2 described image filtering methods, wherein said step 4 can be exchanged with the order of step 5.

Technique scheme 2 described image filtering methods, wherein step 3 and step 4～6 use serial mode, parallel mode or serial to calculate with parallel mode of mixing.

The digital picture of the original image that technique scheme 2 methods are handled for directly collecting, or through the digital picture after certain processing.

Can being applied to of technique scheme 2 is similar in the airspace filter method of non-local mean filter weight nuclear weight calculation method.Step 3a) in, error image can be obtained by any elementary mathematics conversion between all corresponding point between original image and the biasing image.Step 3d) in, weighting nuclear weights can be by image biasing similar function value is obtained by any elementary mathematics conversion.

Be example with technical scheme 1 below, illustrate that filtering method of the present invention can realize the filter effect of non-local mean space domain time varying wave filter:

The rectangular area that is provided with in technical scheme 1 step 1 is shaped as the square that radius is r.

For step 3.1) the error image Δ that obtains ^{(u, v)}(x, y), as shown in Figure 6, if want calculated difference image Δ ^{(u, v)}(x, y) all coordinate points place numerical value sums in the middle rectangular block D can obtain by following formula:

D _s＝A _s+(A+B+C+D) _s-(A+B) _s-(A+C) _s，

D wherein _s, A _s, (A+B+C+B) _s, (A+B) _s, (A+C) _sBe respectively all coordinate place numerical value sums in the respective rectangular scope.

Obviously, A _s, (A+B+C+B) _s, (A+B) _s, (A+C) _sValue be respectively integral image S ^{(u, v)}Middle S ^{(u, v)}(x _l, y _t), S ^{(u, v)}(x _r, y _b), S ^{(u, v)}(x _l, y _b), S ^{(u, v)}(x _r, y _t) value.Contrast step 3.3) as can be known, and D (x, y, u, value v) is the error image Δ ^{(u, v)}(x, y) in so that (x y) is the data sum of the rectangular area at center.Integrating step 3.1) computation process of error image, step 3.3 as can be known) the image biasing similar function value that obtains also can be expressed as:

$D(x,y,u,v)={\left|\right|B_r(x,y)-B_r(x+u,y+v)\left|\right|}_p^p,$

B wherein _r(x, y) for the expression with (x y) is the center, is the matching window of the rectangular block of radius with r, || || _p ^pExpression l _pThe p power of norm value.

Top presentation of results, method of the present invention can obtain the image biasing similar function value identical with existing non-local mean filtering airspace filter device, have also just obtained identical weighting nuclear weights in view of the above.

Obviously, under identical weighting nuclear weights, filtering method of the present invention has identical filter effect with the image filtering method of existing non-local mean space domain time varying wave filter.

Existing non-local mean space domain time varying filtering method is when calculating the weighting nuclear weights of adjacent pixels point and region of search bias combination, the phenomenon that the images match window covers can appear, thereby can cause the matching window interior pixel point that covers and add region of search setovering between the combination of pixels, repeatedly carry out the calculating redundancy issue that relatively calculates.And the present invention is because for each biasing coordinate in the region of search, adopt the step 3.1 of technical scheme 1)～3.4) or the step 3a of technical scheme 2)～3d), for each pixel with add region of search biasing combination of pixels, only calculate once relatively calculating operation, that has eliminated that existing non-local mean space domain time varying filtering method exists covers the problem of the calculating redundancy that causes by matching window.So non-local mean space domain time varying image filtering method that the present invention proposes, under the situation that does not influence filtering performance, greatly reduce the calculated amount of existing non-local mean space domain time varying filtering method, accelerated filtering speed, widened the range of application of non-local mean wave filter.

Quick filter effect of the present invention can further specify by the simulation result of Fig. 7 and Fig. 8.

On 64 GNU/Linux operating systems that run on the 3.0GHz Intel E8400GPU, the image filtering method that proposes with existing non-local mean space domain time varying image filtering method and the present invention respectively is to carrying out the emulation experiment of Filtering Processing as sequence with set of diagrams.The C/C++ programming language that simulated program adopts is realized.

In l-G simulation test, region of search V _RShape is set to the square that radius is R, and the matching window shape is set to the square that radius is r.In similarity relatively under the situation of norm parameter p=1 and p=2, statistics is 4,6,8,10 and 12 in R value respectively, and r is under 2,3,4,5,6 and 7 the situation, the computing time of the filtering method of existing filtering method and the present invention's proposition.The results are shown in Figure 7 during p=1, the results are shown in Figure 8 during p=2.From the result of Fig. 7 and Fig. 8 as can be seen, no matter under p=1 still is the situation of p=2, the method that the present invention proposes is than great reduction is all arranged computing time of existing filtering method; Under fixing R value, increase sharply along with the increase of r the computing time of existing filtering method, and increase with the increase of r the computing time of filtering method of the present invention hardly.Particularly get under the situation of higher value at R and r, the method quick filter effect that the present invention proposes is more obvious.

Claims (8)

1. a non-local mean space domain time varying image filtering method comprises the steps:

(1) obtains original image information, relatively norm parameter p of region of search shape, matching window size, weighting nuclear width h and similarity is set;

(2) the non-normalized filtered image I of initialization (x, y) (x y) is 0, and wherein (x y) is image coordinate with weights normalization coefficient α;

(3) with the point in the region of search as biasing, to the operation of a have execution in step (4)～(9);

(4) (u v) is an amount of bias, calculates the value of the p power of the absolute value of the data difference of all corresponding point between original image and the biasing back image, obtains p norm error image Δ with current biasing ^{(u, v)}(x, y);

(5) (u v) descends the error image Δ to calculate current biasing ^{(u, v)}(x, integral image S y) ^{(u, v)}(x, y), computing formula is:

$S^{(u,v)}(x,y)=\underset{y^{\′}\≤y}{\mathrm{\Σ}}\underset{x^{\′}\≤x}{\mathrm{\Σ}}{\mathrm{\Δ}}^{(u,v)}(x^{\′},y^{\′});$

(6) by following formula calculate current biasing coordinate (u, the v) image at each coordinate place of under the original image similar function value of setovering:

D(x，y，u，v)＝S ^(u，v)(x _l，y _t)+S ^(u，v)(x _r，y _b)-S ^(u，v)(x _l，y _b)-S ^(u，v)(x _r，y _t)，

Wherein, (x y) is image coordinate, (x _l, y _t), (x _r, y _b) represent respectively with (x, y) upper left corner coordinate of the matching window at center and lower right corner coordinate;

(7) by following formula calculate current biasing (u, v) down, the weighting at each coordinate place of original image nuclear weights:

$w(x,y,u,v)=\exp (-\frac{D(x,y,u,v)}{2h^p}),$

Wherein, (u v) is weighting nuclear weights to w for x, y, and h is a weighting nuclear width, and exp () is an exponential function;

(8) current biasing coordinate (u, v) down, upgrade the weights normalization coefficient at each coordinate place of original image by following formula:

α(x，y)＝α(x，y)+w(x，y，u，v)，

Wherein, (x y) is normalization coefficient to α;

(9) under current biasing coordinate, upgrade the non-normalized filtered value at each coordinate place of original image by following formula:

I(x，y)＝I(x，y)+w(x，y，u，v)×I(x+u，y+v)，

Wherein, (x y) is non-normalized filtered value to I, and I is an original image information;

(10) by following formula each coordinate of original image is carried out normalized, obtain image after the filtering

$\hat{I}(x,y)=\frac{\stackrel{\‾}{I}(x,y)}{\mathrm{\α}(x,y)}.$

2. image filtering method according to claim 1, step wherein (8) can be exchanged with the order of step (9).

3. image filtering method according to claim 1, wherein the shape of the described region of search of step (1) is set to rectangle, triangle, circle or arbitrary polygon.

4. image filtering method according to claim 1, wherein step (4)～(9) and step (10) use serial mode, parallel mode or serial to calculate with parallel mode of mixing.

5. a non-local mean space domain time varying image filtering method comprises the steps:

1) obtains original image information, relatively norm parameter p of region of search shape, matching window size, weighting nuclear width h and similarity is set;

2) with the point in the region of search as biasing, to a have execution in step 3)～6) operation;

3) (u v) is an amount of bias, calculates the value of the p power of the absolute value of the data difference of all corresponding point between original image and the biasing back image, obtains p norm error image Δ with current biasing ^{(u, v)}(x, y), wherein (x y) is image coordinate;

4) (u v) descends the error image Δ to calculate current biasing ^{(u, v)}(x, integral image S y) ^{(u, v)}(x, y), computing formula is:

$S^{(u,v)}(x,y)=\underset{y^{\′}\≤y}{\mathrm{\Σ}}\underset{x^{\′}\≤x}{\mathrm{\Σ}}{\mathrm{\Δ}}^{(u,v)}(x^{\′},y^{\′});$

5) by following formula calculate current biasing coordinate (u, the v) image at each coordinate place of under the original image similar function value of setovering:

D(x，y，u，v)＝S ^(u，v)(x _l，y _t)+S ^(u，v)(x _r，y _b)-S ^(u，v)(x _l，y _b)-S ^(u，v)(x _r，y _t)，

Wherein, (x y) is image coordinate, (x _l, y _t), (x _r, y _b) represent respectively with (x, y) upper left corner coordinate of the matching window at center and lower right corner coordinate;

6) by following formula calculate current biasing (u, v) down, the weighting at each coordinate place of original image nuclear weights:

$w(x,y,u,v)=\exp (-\frac{D(x,y,u,v)}{2h^p}),$

Wherein, (u v) is weighting nuclear weights to w for x, y, and h is a weighting nuclear width, and exp () is an exponential function;

7) by following formula calculate each coordinate place of original image weights normalization coefficient α (x, y):

$\mathrm{\α}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}w(x,y,u,v),$

Wherein, (u v) is the coordinate in the region of search, V _RBe the region of search shape, and w (x, y, u, v j) is weighting nuclear weights;

8) by following formula calculate to calculate each coordinate place of original image non-normalized filtered value I (x, y):

$\stackrel{\‾}{I}(x,y)=\underset{(u,v)\∈V_R}{\mathrm{\Σ}}[w(x,y,u,v)\×I(x+u,y+v)],$

Wherein, I is an original image information;

9) by following formula each coordinate of original image is carried out normalized, obtain image after the filtering

$\hat{I}(x,y)=\frac{\stackrel{\‾}{I}(x,y)}{\mathrm{\α}(x,y)}.$

6. image filtering method according to claim 5, the step 7) wherein and the order of step 8) can be exchanged.

7. image filtering method according to claim 5, wherein the shape of the described region of search of step 1) is set to rectangle, triangle, circle or arbitrary polygon.

8. image filtering method according to claim 5, wherein step 3)～6) and step 7)～9), use serial mode, parallel mode or serial to calculate with parallel mode of mixing.

Images